JHPCSN: Volume 4, Number 1, 2012, pp

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1 JHPCSN: Volume 4, Number 1, 2012, pp A REVIEW ON RAIN ATTENUATION OF RADIO WAVES Sumit Joshi 1 1 GRD-IMT, Dehradun, India Abstract: Water is naturally found in atmosphere in three major physical states as: liquid (rain, fog & clouds), solid (snow flakes, ice-crystals) & gaseous (water vapors). In any of the forms the occurrence of water causes hindrances in the path of radio waves in form of absorption & scattering leading to some loss in signal quality & quantity both which is quantified in terms of attenuation. Here we present a brief outlook of how & why rain attenuation takes place & how it is measured & a review of all the methods developed so far for attenuation measurement. Index Terms: Raindrop shape, Rainfall rate, Polarization, Specific Attenuation. 1. INTRODUCTION A radio wave is simply an electromagnetic wave possessing all the characteristics of an electromagnetic wave and in a modern scenario as today when communication technologies are in a head to head race with each other, the impact of rainfall on radio waves becomes significant with respect to QoS issues. The most fundamental among all types of available precipitations is the rainfall and whenever a radio wave passes through a rain particle some of the part of its energy gets absorbed & some of it gets scattered. Therefore, the net attenuation of a radio wave due to rain can be depicted as a combination of attenuation due to absorption & attenuation due to scattering depicted as Figure 1. Thus, we can classify the overall attenuation in signal strength of radio waves due to rain in to two categories: 1. Absorption losses 2. Scattering losses When the wavelength of the radio signal is large enough with respect to the size of the raindrop the effect of scattering is predominant as compared to absorption and in case the wavelength is comparatively smaller than the size of the raindrop than the absorption predominates scattering. 2. RAIN DROP & ITS IMPACT The raindrop molecules behaves as dipoles & these smaller drop dipoles possess time variations which are similar in nature to that of radio waves and thus these acts like a miniature radiator radiating radio waves passing through them but certainly with smaller directivity. This leads to radiating energy in random fashion in numerous directions apart from the direction of receiver which leads to a loss in radio energy along the direction of receiver. Figure 1: Depiction of Causes Contributing to Attenuation of the Radio Waves Due to Rain Moreover, raindrops as stated are polar and thus always the positive polarity portion tends to be in closeness with the negative polarity portion. This means that when a radio wave passes through or near to these they tend to rotate the polarity of these or in other words the water molecule itself pertaining to time variable polarity changes in radio waves. Even more these droplets grow in size dynamically due to a phenomenon known as coalescence as per the facts that the water has high

2 60 Sumit Joshi relative dielectric constant & high specific heat which facilitates binding of these rain drops to each other. 3. RAIN DROP SHAPE Another major issue in attenuation measuring is subjected to the factor of raindrop shape which depends mainly on size of the droplets. Only very small rain drops are considered to be spherical in shape & larger rain drops i.e. the drops with dia. greater than 1mm are considered to be oblate spheroid or flat base spheroids by shape, pertaining to their dynamic state as they start falling down with respect to the environmental forces acting on them. In its final stages the drop shape changes more due to concavity in the drop base. This process of change in topology of a drop from spherical to a radial expanding sheet due to kinematics involved, the drop deforms in its shape as it falls down under the effect of gravity with certain terminal velocity due to which emerges radial entities which later grow in to a number of drops. Different rain drop size exists depending upon intensity of rainfall precipitation for a particular region. Thus, we classify these variable sized rain drops as: Table 1 Classification of Raindrop Shape Based on Rainfall Types Drop Size (in mm) Shape Kinds of rainfall 1 mm-2 mm Nearly spherical Low rainfall >2 mm Flat base spheroid Moderate rainfall >4 mm Concave base Heavy rainfall spheroid Some common rain drop shapes are displayed in Figure 2 below. The rainfall attenuation measurement involves the term called drop-size distribution -DSD. This is due to the fact that the rain drops present in the atmosphere as hydrometeors causes scattering of radio-waves propagating through them. The actual problem of rainfall attenuation prediction deals with initial task of relating two quantities i.e. the rainfall-rate & the attenuation. Sometimes relating attenuation with two distinct polarizations is also used as a prime prediction technique. All these factors are related to the integral of drop-size distribution function represented as N(D), defined mathematically depicting N(D) dd[3] as the number of drops of rain collected per cubic meter with drop size lying between the integration limits of D & D+dD as shown: N (D) dd (1) Generally, the drop shape is taken to be spherical but in certain cases it may be slightly nonspherical, in such cases measurements are carried out considering volume of that of an equivalent equi-volumic sphere, thus N (D) is sometimes also called as the shape factor. Comparison of some of the popular DSD models used for the purpose of attenuation measurement or prediction are depicted as below in form of Table 2. Table 2 Some Earlier Popular DSD Models Used in Study of Attenuation Due to Rain DSD Function type Mathematical Remarks equivalent 1. Exponential N(D)=N 0 exp(- D); Most Preliminary Distribution = 4.1 R 0.21 Model 2. Gamma N(D)=N 0 D m exp More general Distribution (3.67+m) D/D 0 3. Laws-Parson No mathematical Empirical by Distribution representation nature, primitive 4. Marshall-Palmer No mathematical Similar to 3 except Distribution representation larger no. of smaller drops in the spectra. Figure 2: Different Kinds of Common Rain Drop Shapes Observed Naturally These comparisons made in Table 2 depicts that different models for defining rain drop shapes are available and they facilitates computation of contribution of different shaped rain drops to the total average rainfall for a region. Still, it depends up on the climate & other environmental factors for

3 A Review on Rain Attenuation of Radio Waves 61 that region which decides the selection of raindrop distribution functions [1][2]. Specifically, Log-Normal distributions or Gamma distributions are found to be more suitable & accurate for prediction of attenuation via rain from Indian subcontinent perspective. Many models have been proposed for prediction of radio waves attenuation due to rain but these all models are application & site specific & hence a proper optimal choice is to be made before deploying any model for any sort of problem. Thus a summary of different models has been done to facilitate the choice of models as Table 3. Table 3 Summary of Some Popular Rain Related Attenuation Models Model Name Kind of Region of Features Model Deployment Rice- Statistical Temperate Uses cumulative Holmberg Model climates with time Model heavy rainfall. distribution of rainfall. Dutton- Statistical Used for Exceedance Dougherty Model gaseous & rain time % Model attenuation used with both rain rate. Global Statistical Used for Globally Model Model rain only accepted values conditions for rain attenuation parameters Crane Statistical Used for Surface Model Model different point rain hydrometeors rate is the fundamental step. Fixed Statistical Used for Assumes Effective Model a fixed rain 6.6mm/h Rain Model intensity of fixed effective rain intensity over all paths. Variable Statistical Used for Assumes Effective Model variable attenuation Rain rain intensity increases with Model rain intensity CCIR Analytical Used for Assumes Model Model region wise algorithmic (now ITU-R) rain intensity calculation approach for attenuation calculation. 4. FUNDAMENTAL HYDROMETEOR SCATTERING THEORY Any radio wave generation comprises of two most common fields known as: near-field & far-field, of which more significant in view of scattering is the far-field. The scattered field via; any particle is generally a dimensionless entity function of scattering angles so obtained on scattering of the radio-waves & is represented mathematically as: E SCATTERING =E INCIDENT.S(,Φ)/jkr.exp(-jkr+jwt) (2) Where (k = 2π/ ) Where r is the radial distance from the particle. Generally, the total loss cross-section of the particle is given as: C external = 2 /π Re [S (0)] (3) Where S (0) is written for the forward scattering phenomenon encountered. Thus, if we consider a plane wave propagating through a medium which consists of N stochastically distributed particles per unit of volume than the plane wave suffers an attenuation given by the relation as: α (attenuation) = 8.7 N 2 /2π Re[S(0)] db/unit distance. & the phase shift attributed to it is given by the relation as: β (phase shift) =N 2 /2π Im [S(0)]radians/unit distance. Thus, the rain distribution of drop sizes can now be viewed mathematically as a relationship between the shape parameter & scatter parameter in the form depicted as: D N (D) S (0, D) dd (4) The popular Rayleigh scattering criterion is deployed only if the scattering particle size & refractive index n are in the Rayleigh scattering region when the particle is electrically small along with the phase shift encountered being small enough. Rayleigh s approximation assumes the following points: The scattered field is that of a dipole. The induced dipole moment associated with the particle is in relationship with the incident electric field in the same way as for electrostatic fields[4].

4 62 Sumit Joshi Rayleigh scatter criterion is used specifically for cloud droplets & atmospheric crystals of ice & thus leads a partial way in to rain related attenuation. 5. CONCEPT OF DEPOLARIZATION The non-spherical raindrop has another effect, known as depolarization. Small rain drops are spherical but for diameters above 4mm, the base becomes concave. Therefore different polarizations come in to being & thus will propagate at different speeds through air containing rain and this will lead to differential phase shifts. They will also experience differential attenuation. Below 15 GHz most of the depolarization comes from the differential phase shift and above 15 GHz most of the depolarization comes from the differential attenuation [7]. If the polarization plane (E-Field Vector) coincides with the symmetry of the raindrop, not a lot will change apart from the horizontally polarized signal will be delayed relative to the vertical signal. If the drop is not aligned with the polarization, for example if the drop is rotated by winds or if the polarization is slant or circular, energy will be transferred between the polarization states. It is a good assumption for rain to assume the symmetry planes are close to vertical and horizontal, so H & V polarized signals will not be depolarized by very much but slant polarized and circular polarized signals may be. drop-size distribution function N ( D) the total attenuation obtained is computed as: A = 4.34 L+ C ext N (D) dd decibels (5) 7. POLARIZATION DEPENDENCE Because of hydrometeors not being perfectly spheroids, a wave propagating through them generally experiences a polarization change along LOS as it travels through & this cross polarity may lead to severe consequences in case of communication systems deploying polarization orthogonality to maintain isolation between channels. E.g. LMDS with polarity considerations. 8. PRINCIPLE PLANES & POLARIZATION BASICS For a definite volume hydrometeors on a los path there are two types of polarizations which propagate over the link. These polarization are frequency dependant & vary with time as the amount of rainfall changes. The two of the polarizations are called principal planes; therefore the waves transmitted in direction of principle planes are transmitted without any change but due to absence of perfect non-spheroid drop particles, the wave s experience different attenuation & phase shift pertaining to the fact that the actual shape of drops is oblate-spheroid. Thus, it is assumed for the sake of rotational symmetry in the wave via. Drop; that symmetry axes are vertical i.e. the principal planes are linearly vertical & horizontal. This account for a good approximation for most of the analysis cases as has been found in earlier works. Some important points regarding attenuation: (i) A raindrop poses a mean shape close to that of an oblate-spheroid & thus attenuation suffered by a plane wave is differential by nature. (ii) At lower frequencies of operation it has been found in earlier works that the Rayleigh approximation holds good, which also Figure 3: Depiction of Raindrop & Scattering Due to it 6. TOTAL RAIN ATTENUATION EFFECTS The total attenuation offered due to the rain is generally depicted as summation of the contribution from each & every drop. Thus considering the The studies so far reveal that the impact of rain below 5 GHz frequency is of nearly null significance in terms of attenuation effects pertaining to radio propagation but it has also been reviewed that for higher rain rates the attenuation even at lower frequency of operation becomes significant.

5 A Review on Rain Attenuation of Radio Waves 63 suggests that attenuation & phase shift along horizontal polarization direction is found to be more than vertical. (iii) Attenuation effects & phase shift below 18 GHz are found to increase with frequency for a given rainfall-rate & a decrease in values have been observed for a given fadedepth due to the fact pertaining that smaller drops make a greater relative donation to the net attenuation as the frequency accelerates. 9. SPATIAL-TEMPORAL RAIN OUTLOOK Another key factor in determining the attenuation suffered by a radio wave is the rainfall-rate. The most popularly used statistical parameters are those of annual rainfall, defined as rain-rate exceeding for a given % of yearly time. Generally, the rainfall values observed over different locations vary largely & thus averaged statistics is preliminary preferred over many years of analysis data. It may somehow be possible that the values obtained are not in fine alignment or the data may not be sufficiently accurate, for the same ITU-R Recommendations[9] are the boon as they provide annual statistics for the whole world depending on latitude-longitude value of that place on earth s surface. 10. FUNDAMENTAL APPROACHES FOR ATTENUATION CALCULATION The most common techniques for calculation of rain related attenuation effect encompasses two fundamental methodologies as: (a) Deploying uniform random distribution of rain drop modeled as some specific shape & thus calculating the orientation related effects due to drop shape[8]. (b) An empirical formulation relating rainfall rate with specific attenuation as: Firstly, we focus on approach (b) where relationship between the rainfall rate & specific attenuation is depicted as: A = a R b (6) Where R is the rainfall rate in mm/h and a & b are the parameters which area function of frequency & polarization whose values are obtained via, experiments. Further, the procedure to calculate this important entity called rainfall rate follows as: (a) Conversion of rain precipitation data in to exceedance rain rate is the primary step. This is done by dividing the rainfall precipitation data ( in mm) by observation time period as depicted: R (rainfall rate mm/h) = D (precipitation mm)/observation-time (in hours). (b) Next we compare the values of R with nearest rain rate exceeded values (R q ) such that Re R q, thereafter this value is the value corresponding to the maximum exceeded rain rate for that case of consideration[9]. (c) Now we calculate the number of hours or minutes or seconds for the case of concern such that for this much of time the rain rate exceeds a nearest rain rate value (R q )[5]. (d) Thus overall number of hours in a year for which rain rate exceeds the value R q mm/h is obtained by adding all the individual cases as depicted: D (R q ) = Σ D rq (7) Where D denotes duration and r is the r th case of consideration for which the rainfall rate was found to exceed. The other values in between which are found to be escaping out can easily be traced by using curve-fitting deploying least squares methodology keeping in view the log normal distribution predominantly used to approximate the rainfall rate distribution. Furthermore, we can classify local region based on outage measurements in to subdivisions with similar outage values & can develop rainfall map which facilitates attenuation prediction & better network planning. Now, we focus on approach (a) which is based on rain drop modelling and follows as: (a) Firstly, the calculation of scattered E-field component of the radio waves is carried out. Thereafter based on the values of calculated E-field scattering functions are generated for different drop shapes. (b) Then an important parameter called the rain water permittivity for different frequency of operation is measured & noted. (c) Based on the permittivity values & temperature values (generally water temperature ranges 0 º C-25 º C) the further calculations are carried out.

6 64 Sumit Joshi (d) Furthermore scattering functions are used to relate attenuation with parameters such as drop-size distribution, rain-fall rate, polarization etc. [4]. (e) Finally, the obtained attenuation values are plotted against rainfall rate values at different temperatures. Thus, giving an idea of attenuation for different rainfall rate regions. 11. CONCLUSION Some fundamental observations after a detailed literature review of the attenuation pertaining to the rain related effects are as: 1. The rain related attenuation can be modelled by means of any of the two methodologies as discussed but mostly the approach (b) is preferred because of large database usually available. 2. Most of the previous works indicate that the attenuation results obtained are of significance only over 5-10GHz of operational frequency [7]. 3. Rain drop based modeling of the attenuation is more accurate in sense of exactness. 4. More better methodologies incorporating different factors which are seldom considered like referenced polarizations, present weather conditions, topology of the region concerned etc. are to be incorporated via, some kind of computing approach incorporating along with factors which actually determine network quality in sense of applicability like: throughput, delay etc. REFERENCES [1] Wei Zhang, Nader Moayeri, Power-Law Parameters of Rain Specific Attenuation, Project-IEEE Wireless Access Working Group, National Instiute of Standards & Technology, 26 Oct [2] Wei Zhang, Nader Moayeri, Recommendation: Use of Various Raindrop Size Distributions for Different Geographical Locations in Calculating the Rain Specific Attenuation, IEEE Wireless Access Working Group, National Instiute of Standards & Technology, [3] Ondrej Fiser, The Role of DSD and Radio Wave Scattering in Rain Attenuation, Institute of Atmospheric Physics, Academy of Sciences of Czech Republic, Czech Republic, Geoscience and Remote Sensing, New Achievements, Date created: , book chapter. [4] Rainfall Runoff Relationships, The Science of Surface & Ground Water, Module-2, lesson-3, Version-2 CE, IIT-Kharagpur, NPTEL Lecture Notes. [5] Charles E. Mayer, Bradley E. Jaeger, Rain Attenuation Model Comparison And Validation, Online Journal of Space Communication, Applications, Issue No. 2, Fall [6] Dusan Cermak, Ondrej Fiser, Vladimir Schejbal, Electromagnetic Scattering by Rain Drops, Cost280, Unpublished. [7] Uzma Siddique, Laeeq Ahmad, and Gulistan Raja, Microwave Attenuation and Prediction of Rain Outage for Wireless Networks in Pakistan s Tropical Region, Hindawi Publishing Corporation, International Journal of Microwave Science and Technology, Volume 2011, Article ID , 6 pp. doi: /2011/ [8] N. A. Sontakke, H.N. Singh, Nityanand Sing, Chief Features of Physiographic Rainfall Variations Across India during Instrumental Period ( ), Research Report No. RR-121, ISSN , Contribution from IITM-Pune. [9] R. A. Dalke, G.A. Hufford, R.L. Ketchum, Radio Propagation Considerations for Local Multipoint Distribution Systems, NTIA Report , U.S. Department of Commerce. [10] S. Selim Seker, A. Yasin Citkaya, EM Discrete Approach for Rainfall Attenuation of Propagation, /11, 2011 IEEE.